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hw_prj_4

# hw_prj_4 - Dr Atilla Dogan MAE 4310 Automatic Control Fall...

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Dr. Atilla Dogan MAE 4310 Automatic Control – Fall 2006 Homework–4 (Due date: Thursday, Oct 12, 2006) Textbook Readings: Examples A–5–7, A–5–9, A–5–11, A–5–12, A–5–14 1. (i) Find the dominant poles of the following systems using partial fraction expansions. You may use MATLAB. (a) G ( s ) = s 2 + 1 . 2 s + 3 . 1 s 3 + 11 s 2 + 13 s + 30 (b) G ( s ) = s + 2 . 1 s 4 + 10 s 3 + 41 s 2 + 76 s + 52 (c) G ( s ) = s - 1 . 2 s 3 + 11 s 2 + 8 s - 20 (ii) Use MATLAB to generate pole-zero maps for systems (a)-(c). Circle the dominant poles and indicate any pole-zero cancellations or approximate cancellations. 2. Draw the pole zero map of the following system. Based on the locations of the poles and zeros in the complex plane, approximate this 6 th order system by 4 th , 3 rd and 1 st order systems. Ensure that the approximate systems have the same DC gain as the original system. Plot the step responses of the original and the approximate systems on the same figure. G ( s ) = s 2 + 6 . 2 s + 37 . 7 s 6 + 24 s 5 + 247 s 4 + 1518 s 3 + 5486 s 2 + 10944 s + 8840 3. Determine TF from R to C for the following systems. a) b) Mechanical and Aerospace Engineering - UTA 1 of 4

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Dr. Atilla Dogan MAE 4310 Automatic Control – Fall 2006 c) d) Determine TF from R 2 to C for the following system.
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hw_prj_4 - Dr Atilla Dogan MAE 4310 Automatic Control Fall...

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